Question

Calculate (by hand) the appropriate truth table to prove or disprove the following:
(p → q) ∧ (¬p → r) ⇒ (q ∨ r)
If it is invalid, give a counterexample; otherwise, explain why it is valid.

Answer 1

As, $[(p → q) ∧ (¬p → r)] \to (q ∨ r)$ is a Tautology (always true) ;

Thus; the implication holds.

$\therefore (p → q) ∧ (¬p → r) ⇒ (q ∨ r)$

It is valid as the condtional is a Tautolgy; hece the Implication holds.